**'org.jscience.mathematics.vector.LUDecomposition'**Java class

## Class LUDecomposition<F extends Field<F>>

- java.lang.Object
- org.jscience.mathematics.vector.LUDecomposition<F>

public final class LUDecomposition<F extends Field<F>>extends Object

This class represents the decomposition of a

`matrix`

`A`

into a product of a`lower`

and`upper`

triangular matrices,`L`

and`U`

respectively, such as`A = P\xc2\xb7L\xc2\xb7U`

`with`

`P`

`a`

`permutation`

matrix.This decomposition is typically used to resolve linear systems of equations (Gaussian elimination) or to calculate the determinant of a square

`Matrix`

(`O(m\xc2\xb3)`

).Numerical stability is guaranteed through pivoting if the

`Field`

elements are`numbers`

For others elements types, numerical stability can be ensured by setting the`context-local`

pivot comparator (see`setPivotComparator(java.util.Comparator<org.jscience.mathematics.structure.Field>)`

).Pivoting can be disabled by setting the

`pivot comparator`

to`null`

(`P`

is then the matrix identity).`See Also:`

`Wikipedia: LU decomposition`

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